Flights
There are hundreds of comparison flights now, the below are my favourite, aside from booking direct with the airline. Keep in mind that flight comparison tools don't always factor in all the budget airlines, so if you know your dates or have narrowed your search, it's worth checking direct with the airlines.
Ita Matrix
The best tool I have found for booking flights is ITA Matrix Software, and in my opinion it's incredibly underrated. Done by Google (and potentially stopping soon), this allows you to search by multiple airports, multiple night stays, and across periods (ie. best time to fly in November). You can't book on it directly but it leads you to the various airlines where you can book. Fantastic travel tool and also allows you to email itineraries when you're looking at options.
Expedia
I've found some incredible deals with Expedia that I haven't found anywhere else, including the airlines' own website. I'm really cautious on third-party booking websites but I fully back Expedia. On more than one occasion I've had a problem with a flight booked (delay, date moved, etc.) and Expedia helped me sort my problem with the airline when I couldn't get a hold of the airline directly. I've always found their customer service friendly and professional. If I'm travelling with someone and doing a city break or plan to stay in one place near the airport, I highly recommend the flight + hotel packages for some big savings.
SkyScanner
For me, Skyscanner is good for an overview, but not more than that. I would really warn anyone using Skyscanner to do their homework if they follow and book through a third-party booking website by using Google Reviews or Trustpilot. It may look like you're saving $100 on a long-haul flight but there are horror stores of people 'purchasing' the fares and never getting their actual ticket, resulting in a much higher ticket in the end. This is not Skyscanner but rather some of the websites it advertises.
StaTravel
If you are under 26, 31 or a student, it's work checking out STA Travel. They don't always look competitive, but if you are elegible you may be able to get some great fares, plus they don't penalise as heavily for one-way fares. I've had great luck booking one-way, short notice trips, which airlines usually charge extortionate amounts for (Beijing > Venice for £325 one way, Hong Kong > Bologna last minute around £350 one way and with Emirates.
Asia
In Asia, if you're doing short-haul flights, it may pay to fly budget and book directly with the airline.
- Air Asia (Budget, based in Kuala Lumpur, very reasonable fares especially when booked in advance. In my experience, great service. Fan of the in-flight magazine as well, which offers travel tips to destinations around Asia)
- Spring Airlines (Budget. China + Asia - more details in China section)
- Scoot (Budget, Singapore + international). I flew with them when they were Tiger, and they were lovely. Now Tiger only flies in Australia
Philippines
- Cebu Pacific (Budget. cover all parts of the Philippines as well as select cities in Asia and some Oceania; charge separately for luggage. Smiley attendants with occasional 'competitions' on board)
- Philippine Airlines (Philippines, international)
Singapore
- Singapore Airlines (Singapore, international). Have not flown with them myself but have heard they're amazing
- Scoot (see Asia) connects a lot of Singapore
China
There are LOADS of airlines in China so I haven't written or hyperlinked them all. It pays to check if your origin or arrival city / province have one (ie. Chengdu > Chengdu Airlines or Sichuan Airlines) + whether they are part of the airmiles program you're with (more and more, they are joining)
- Spring Airlines (Budget. China + Asia. No two ways about it - they are a terrible, terrible airline, with terrible seating, passengers, stewards and delays. But boy are they cheap. I have not and would not try them long-haul.
- China Eastern (you may need to set the language to English in the Menu tabs). Think CE are part of SkyTeam now which means airmiles if you're part of that club. I've flown long-haul with them before. They're no Emirates, but they're OK.
- China Southern (China, international)
- AirChina (China, international)
- China Airlines (China, international), also part of SkyTeam now
Off the top of my head, some others: Chongqing Airlines, Xiamen Airlines, Chengdu Airlines, Shenzhen Airlines (Star Alliance), Hainan Airlines